What a cutie! Congratulations on your new pup.
Maximo has slept with his head hanging out of his bed onto the floor from the time he was a wee pup. I saw his breeder's pics of the litter and he was the only one doing it, lol. He does it less as an adult. Nothing to worry about.
Relative to the itchies, have you taken her in for her wellness exam at the vet? You will probably be going sometime soon for more vaccinations. Be sure to mention the itching to the doc. You can bathe her anytime. Use a good shampoo and conditioner formulated for dogs.
Preventing water from getting in the ears, and soap from getting is a bit of a trick. Go easy with soap on top of the head and rinse mostly front to back of head. Then down the front. Some people put cotton balls in the ears or plugs. I hold the ear flap down and then use an ear cleaner with a drying agent afterwards.